(1 point) You are visiting your friend Fabio\'s house. You find that, as a joke,
ID: 2893876 • Letter: #
Question
(1 point) You are visiting your friend Fabio's house. You find that, as a joke, he filled his swimming pool with Kool-Aid mixture, which dissolved into the water perfectly. However, now that you want to swim, you must remove all of the Kool-Aid contaminated water. The swimming pool is round, with a 11 foot radius. It is 7.5 feet tall and has 5 feet of water in it. How much work is required to remove all of the water by pumping it over the side? (Use the physical definition of work, and the fact that the weight of the Kool-Aid contaminated water is =64.3lbs/ft3 )
Explanation / Answer
The swimming pool is round, with a 11 foot radius. It is 7.5 feet tall and has 5 feet of water in it.
r=11
let the thickness of thin layer =dx
0x5
distance the layer to be moved =7.5-x
weight of thin layer= 64.3**112dx
amount of work reqired =[0 to 5]64.3**112*(7.5-x)dx
amount of work reqired =[0 to 5](64.3**112)(7.5x-(1/2)x2)
amount of work reqired =(64.3**112)[(7.5*5-(1/2)52)-(7.5*0-(1/2)02)]
amount of work reqired =(64.3**112)[(37.5-12.5)-(0)]
amount of work reqired =64.3**112*25
amount of work reqired =611063.333 lb-ft
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